Temperature of Mixing Water

Introduction

In this activity, you will investigate how to predict the temperature when water at different temperatures are mixed.

How could a pet store manager with a 50-liter tank raise one degree Celsius without adding more than 5 liters to the tank?

When a cold mountain stream flows into a large, warm lake, think about the effect the cold mountain stream has on the temperature of the lake. This is very similar to the situation a pet store manager faces when he adds a liter of cold water to a warm 50-liter fish tank to replenish the water supply.

What effect does the added water have on the temperature of the tank water?

Try to write a rule for predicting the resulting temperature when two quantities of water at different temperatures are mixed.


Standards

NSES Physical Science Ð Transfer of Energy
Energy is a property of many substances and is associated with heat, light, electricity, mechanical motion, sound, nuclei and the nature of a chemical. Energy is transferred in many ways.

NSES Physical Science Ð Transfer of Energy
Heat moves in predictable ways, flowing from warmer objects to cooler ones, until both reach the same temperature.


Materials

  • 3 large foam cups (500 ml or 16 oz)
  • 1 small foam cup (250 ml or 8 oz)
  • 2 empty 35 mm film canisters Ñ or some other measuring device (e.g., graduate cylinder, beaker, etc.)
  • cold water
  • warm water, 30-40 degrees Celsius (80-100 degrees Fahrenheit)
  • large pitchers or jugs

Safety

The warm water in this investigation cannot exceed 40 degrees Celsius (or 100 degrees Fahrenheit). If the water temperature exceeds this temperature, burns may result.


Procedure

  1. Obtain 1 small and 1 large foam cup.
  2. Fill the small cup half full with cold water with no ice cubes.
  3. Place about the same amount of the warm water in the large cup.
  4. Connect the temperature sensor to the computer.

Prediction I

What do you think the temperature will be when you mix cold water with about the same amount of warm water? How did you come up with your prediction?


Collect Data I

Place the temperature sensor in the small cup filled with cold water. Create a new dataset, using the New button on the left and label it ÒcoldÓ water. Measure the temperature by clicking on the Start button in the top graph below. When recording the temperature, wait until the temperature read by the sensor stops changing. Then click the Stop button and record the temperature.

Create a new dataset, using the New button on the left and label it ÒwarmÓ water. Repeat the process for the large cup of water that contains the warm water, and record your results.

Write down the temperatures of the cold and warm water.


Prediction II

Now that you know the temperatures of the hot and cold water, predict the following on the prediction graph beneath your first graph by using the pencil tool. Draw what you think the temperature graph will look like if you:

a. measure the cold water for 10 seconds;
b. measure the warm water for 10 seconds;

c. mix the two together and measure the temperature of the mixture.


Collect Data II

Test your prediction by:

a. measuring the cold water for 10 seconds.
b. measuring the warm water for 10 seconds.
c. pouring the small cup of water into the large cup. Measure and record the temperature of the mixture.

Write down the three measurements.

How good was your prediction?


Collect Data III

Repeat this entire experiment, but with unequal amounts of water. Measure and record the temperature of the mixed water by create a new dataset each time by:

a. measuring and recording the temperature of two film canisters of cold water in a foam cup.
b. measuring and recording the temperatures of one film canister of warm water in a foam cup.
c. pouring the two cups of water together and measure and record the temperature of the mixed water.

Write down the three temperatures:

a. cold water

b. warm water

c. mixture


Analysis

Review your datasets, descriptions of images and previous responses to help answer the following questions.

  1. Is the temperature of your first mixture (two quantities that are about equal) close to what you expected? Explain.

2. Is the temperature of your second mixture (two quantities that are not equal) close to what you expected? Explain.

3. Can you come up with an equation that could help someone else accurately predict the final temperature for mixing two equal volumes of water, knowing only the initial temperatures? Compare this with your measured result.

4. Using the same reasoning, can you write an equation for the final temperature for mixing two parts cold with one part warm water? Compare this with your measured result.

5. Can you come up with an equation that could help someone else accurately predict the final temperature of a mixture of two different volumes of water, if they know the initial temperatures and volumes?


Conclusion

How could a pet store manager with a 50-liter tank raise one degree Celsius without adding more than 5 liters to the tank? Be specific about how much water would he use and at what temperature the water should be.


Second Career STEM Question

A hydrologist must have knowledge of how water mixes when it comes from two different sources such as a river and an ocean.Ê

How might snow melting into a pond during the spring affect the temperature of the pond after a day? After a week? After a month?


Further Investigation

Test your understanding of mixing water at different temperatures.

Prepare a large volume of cold water, say 1 liter. Prepare a smaller volume of very warm tap water. Measure the temperature of both volumes. Measure the volume of warm water that must be added to the cold water to warm it one degree C.

Before testing your theory, predict how much this volume should be.

Write down your measurements:

a. the volume of cold water

b. the temperature of cold water

c. the temperature of warm water

d. the volume of warm water needed to raise the mixture one degree C.

Compare your result with your prediction.